In this paper, an iterative method for solving the minimum Frobenius norm residual problem
with an unknown reflexive matrix with respect to a generalized reflection matrix is introduced, where the matrices and satisfy , and by definition. With any initial reflexive matrix , the matrix sequence converges to its solution within at most steps, theoretically. In addition, if
is used for the initial reflexive matrix with arbitrary matrices , the solution is the least Frobenius norm solution. The numerical experiments support theoretical results.